SOLUTION: A rectangluar swimming pool is 16 ft by 40ft. A tarp to go over the pool also covers a strip of equal width surrounding the pool. If the area of the tarp is 1100 ft, how wide is t

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A rectangluar swimming pool is 16 ft by 40ft. A tarp to go over the pool also covers a strip of equal width surrounding the pool. If the area of the tarp is 1100 ft, how wide is t      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 119122: A rectangluar swimming pool is 16 ft by 40ft. A tarp to go over the pool also covers a strip of equal width surrounding the pool. If the area of the tarp is 1100 ft, how wide is the covered strip around the pool, round to the nearest tenth of a foot.
Found 2 solutions by checkley71, edjones:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
THE TARP HAS THE FOLLOWING DIMENTIOS:
(16+2X)(40+2X)=1100 WHERE X=THE WIDTH OF THE STRIP.
640+80x+32x+4x^2=1100
4x^2+112x+640-1100=0
4x^2+112x-460=0
4(x^2+28x-115)=0
using the quadratic equation x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ we get
x=(-28+-sqrt[28^2-4*1*-115])/2*1
x=(-28+-sqrt[784+460])/2
x=(-28+-sqrt1244)/2
x=(-28+-35.27)/2
x=(-28+35.27)/2
x=7.27/2
x=3.64 answer for the width of the strip.

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let x the width of the covered strip around the pool.
(x+16)*(x+40)=1100
x^2+56x+640=1100
x^2+56-460=0
The width of the strip is 7.3 ft (see below)
.
Ed
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B56x%2B-460+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2856%29%5E2-4%2A1%2A-460=4976.

Discriminant d=4976 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-56%2B-sqrt%28+4976+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2856%29%2Bsqrt%28+4976+%29%29%2F2%5C1+=+7.27038417709679
x%5B2%5D+=+%28-%2856%29-sqrt%28+4976+%29%29%2F2%5C1+=+-63.2703841770968

Quadratic expression 1x%5E2%2B56x%2B-460 can be factored:
1x%5E2%2B56x%2B-460+=+%28x-7.27038417709679%29%2A%28x--63.2703841770968%29
Again, the answer is: 7.27038417709679, -63.2703841770968. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B56%2Ax%2B-460+%29